Non-uniqueness of ergodic measures with full Hausdorff dimension on a Gatzouras-Lalley carpet
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math.CA
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carpetdimensionergodicfullgatzouras-lalleyhausdorffmeasuresanswer
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In this note, we show that on certain Gatzouras-Lalley carpet, there exist more than one ergodic measures with full Hausdorff dimension. This gives a negative answer to a conjecture of Gatzouras and Peres.
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